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Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
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Introduction to geometric processing through optimization.

Gabriel Taubin

    IEEE Computer Graphics and Applications
    |May 9, 2014
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces geometry processing techniques to solve equations using least-squares methods. It enables practical, interactive polygon mesh editing through basic optimization strategies.

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    Area of Science:

    • Computer Graphics
    • Computational Geometry
    • Applied Mathematics

    Background:

    • Interactive editing of polygon meshes is crucial in computer graphics.
    • Existing methods may lack efficiency or simplicity for practical applications.
    • Formulating geometric operations as systems of equations is a common approach.

    Purpose of the Study:

    • To present a method for formulating geometry processing operations as least-squares problems.
    • To develop simple, practical tools for interactive polygon mesh editing.
    • To provide a foundation for implementing more advanced algorithms.

    Main Methods:

    • Deriving equations from local geometric relations using analytic geometry concepts (points, lines, planes, vectors, polygons).
    • Applying basic descent strategies to solve the resulting optimization problems.
    • Incrementally developing mathematical formulations for software implementation.

    Main Results:

    • Successful formulation of geometry processing operations as least-squares systems.
    • Development of simple, effective tools for interactive polygon mesh editing.
    • Demonstration of practical implementation of these mathematical concepts.

    Conclusions:

    • The proposed least-squares approach provides a viable method for interactive polygon mesh editing.
    • The presented mathematical formulations are suitable for implementing practical software.
    • The work serves as a basis for readers to explore and implement higher-performance algorithms.